NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 06:45 It is currently 26 Apr 2024, 06:45
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If n is a three-digit positive integer, what is the tens digit of n?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
CAMANISHPARMAR
VP
VP
Joined: 12 Feb 2015
Posts: 1065
Own Kudos [?]: 2103 [42]
Given Kudos: 77
Send PM
If n is a three-digit positive integer, what is the tens digit of n? [#permalink] New post   21 May 2018, 00:32
3
Kudos
39
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

34% (02:33) correct 66% (02:24) wrong based on 335 sessions
Hide Show timer Statistics
If n is a three-digit positive integer, what is the tens digit of n?

(1) Dividing n by 4 gives the same remainder as does dividing n by 25.
(2) Dividing n by 16 gives the same remainder as does dividing n by 25.
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11181
Own Kudos [?]: 31947 [7]
Given Kudos: 290
Send PM
Reviews Badge
Re: If n is a three-digit positive integer, what is the tens digit of n? [#permalink] New post   07 Jun 2018, 05:33
4
Kudos
3
Bookmarks
Expert Reply
CAMANISHPARMAR wrote:
If n is a three-digit positive integer, what is the tens digit of n?

(1) Dividing n by 4 gives the same remainder as does dividing n by 25.
(2) Dividing n by 16 gives the same remainder as does dividing n by 25.


IMPORTANT :-
when can two numbers leave same remainder - when we are looking at the numbers after their LCM or x*LCM, where x is a positive integer

(1) Dividing n by 4 gives the same remainder as does dividing n by 25.
so the numbers should be immediately after the LCM of 4 and 25, which is 100..
and remainder of 4 can be 0,1,2,3.... so numbers can be 100,101,102,103
next will be 2*100, 201,202,203
so in all cases the TEN's digit will be 0
sufficient

(2) Dividing n by 16 gives the same remainder as does dividing n by 25.
so the numbers should be immediately after the LCM of 16 and 25, which is 400..
and remainder of 16 can be 0,1,2,3...15, so numbers can be 400,401,402,403,....410,411,..415
next will be 2*400, 801,802,803...810,811...815
so in all cases the TEN's digit will be 0 or 1
insufficient

a
General Discussion
User avatar
P
GyMrAT
Senior Manager
Senior Manager
Joined: 14 Dec 2017
Posts: 426
Own Kudos [?]: 459 [4]
Given Kudos: 173
Location: India
Send PM
Re: If n is a three-digit positive integer, what is the tens digit of n? [#permalink] New post   05 Jun 2018, 12:03
3
Kudos
1
Bookmarks
CAMANISHPARMAR wrote:
If n is a three-digit positive integer, what is the tens digit of n?

(1) Dividing n by 4 gives the same remainder as does dividing n by 25.
(2) Dividing n by 16 gives the same remainder as does dividing n by 25.



Given n is a three digit number, required is tens digit of n.

Statement 1:
Let \(r\) be remainder, then
\(n = 4k + r\), \(0<=r<4\)
\(n = 25q + r\), \(0<=r<25\)

Hence \(0<=r<4\), \(r = 0,1,2,3\)

LCM of \(4\) & \(25\) is \(100\), hence \(n = 100p + r\)

So r will be units digit of a multiple of 100, hence the tens digit of n will be 0.

Statement 1 is sufficient.

Statement 2:
Let \(z\) be remainder, then
\(n = 16x + z\), \(0<=z<16\)
\(n = 25y + z\), \(0<=z<25\)

Hence \(0<=z<16\), \(z = 0,1,2,3,4,....15\)

LCM of \(16\) & \(25\) is \(400\), hence \(n = 400w + z\)

So if \(z<10\), \(z\) will be units digit of a multiple of \(400\), hence the tens digit of \(n\) will be \(0\).
& if \(z>=10\), then last digit of 2 digit number \("z"\), will be the units digit of a multiple of \(400\) & the tens digit will be \(1\).

Hence 2 values for the remainder.

Statement 2 is Insufficient.

Answer A.


Thanks,
GyM
User avatar
L
CAMANISHPARMAR
VP
VP
Joined: 12 Feb 2015
Posts: 1065
Own Kudos [?]: 2103 [3]
Given Kudos: 77
Send PM
If n is a three-digit positive integer, what is the tens digit of n? [#permalink] New post   21 May 2018, 00:42
1
Kudos
2
Bookmarks
Question Stem:- n is a three-digit positive integer. To find - what is the tens digit of n
Important points:-
Its a value question.

STATEMENT 1:-

First find LCM 4 & 25 ---> 100. Check which all three digit numbers will give same remainder when divided by 100. e.g. 101, 102, 103, 201, 202, 203 ...... 901, 902, 903 etc. These are different numbers but look what the question stem is asking? Its asking for tens digit hence we have a definite value, its 0. hence statement 1 is sufficient.

We are down to A vs D.

Statement 2:-
Repeat the same process, First find LCM 16 & 25 ---> i.e. 400. Check which all three digit numbers will give same remainder when divided by 400. e.g. 401, 402, 403, .....414,415......... 801, 802, 803....814, 815.... etc. These are not only different numbers but this time we don't even have a tens digit which has a definite value, it can be 0 or 1. hence statement 2 is insufficient.

Hence the correct answer is A
User avatar
G
Masterscorp
Manager
Manager
Joined: 14 Oct 2017
Posts: 192
Own Kudos [?]: 271 [1]
Given Kudos: 385
GMAT 1: 710 Q44 V41
Send PM
Re: If n is a three-digit positive integer, what is the tens digit of n? [#permalink] New post   05 Jun 2018, 10:25
1
Kudos
Nice question but it should be moved to the DS section :)
avatar
P
Shobhit7
Manager
Manager
Joined: 01 Feb 2017
Posts: 246
Own Kudos [?]: 346 [1]
Given Kudos: 148
Send PM
Re: If n is a three-digit positive integer, what is the tens digit of n? [#permalink] New post   07 Jun 2018, 05:13
1
Kudos
St.1: Divisors 4 and 25.
Possible Remainders 0 to 3.
LCM of 4 and 25 is 100

For Remainder 0:
Common no. 100, 200 to 900
(Adding LCM to first common no.)

For Remainder 1: 101 to 901
For Remainder 2: 102 to 902
For Remainder 3: 103 to 903

In all of the above, tens digit is 0. SUFFICIENT.

St.2: Divisors 16 and 25.

So, with divisor 16, Remainders range is from 0 to 15.

Hence, tens digit can be either 0 or 1. INSUFFICIENT.

Therefore, Ans A

Posted from my mobile device
User avatar
L
CAMANISHPARMAR
VP
VP
Joined: 12 Feb 2015
Posts: 1065
Own Kudos [?]: 2103 [0]
Given Kudos: 77
Send PM
Re: If n is a three-digit positive integer, what is the tens digit of n? [#permalink] New post   05 Jun 2018, 10:28
Masterscorp wrote:
Nice question but it should be moved to the DS section :)


Thanks, I have already informed the administrators to do the needful but they have not moved it yet :)

Thanks again!!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92933
Own Kudos [?]: 619171 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: If n is a three-digit positive integer, what is the tens digit of n? [#permalink] New post   05 Jun 2018, 10:29
Expert Reply
Masterscorp wrote:
Nice question but it should be moved to the DS section :)


Moved to DS forum. Thank you.
User avatar
L
CAMANISHPARMAR
VP
VP
Joined: 12 Feb 2015
Posts: 1065
Own Kudos [?]: 2103 [0]
Given Kudos: 77
Send PM
Re: If n is a three-digit positive integer, what is the tens digit of n? [#permalink] New post   05 Jun 2018, 11:19
Bunuel wrote:
Masterscorp wrote:
Nice question but it should be moved to the DS section :)


Moved to DS forum. Thank you.


Thanks Bunuel
avatar
B
samstthomas
Intern
Intern
Joined: 24 Feb 2019
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 12
Location: United Kingdom
Schools: LBS '22 (D) IMD '21
Send PM
Re: If n is a three-digit positive integer, what is the tens digit of n? [#permalink] New post   03 Nov 2019, 13:38
CAMANISHPARMAR wrote:
Question Stem:- n is a three-digit positive integer. To find - what is the tens digit of n
Important points:-
Its a value question.

STATEMENT 1:-

First find LCM 4 & 25 ---> 100. Check which all three digit numbers will give same remainder when divided by 100. e.g. 101, 102, 103, 201, 202, 203 ...... 901, 902, 903 etc. These are different numbers but look what the question stem is asking? Its asking for tens digit hence we have a definite value, its 0. hence statement 1 is sufficient.

We are down to A vs D.

Statement 2:-
Repeat the same process, First find LCM 16 & 25 ---> i.e. 400. Check which all three digit numbers will give same remainder when divided by 400. e.g. 401, 402, 403, .....414,415......... 801, 802, 803....814, 815.... etc. These are not only different numbers but this time we don't even have a tens digit which has a definite value, it can be 0 or 1. hence statement 2 is insufficient.

Hence the correct answer is A




Hi, for the statement A, if I chose the number as 150. The remainder is 2 when divisible by 4 and 25. In which, case the there are two outcomes isnt it? Please clarify
User avatar
L
CAMANISHPARMAR
VP
VP
Joined: 12 Feb 2015
Posts: 1065
Own Kudos [?]: 2103 [0]
Given Kudos: 77
Send PM
Re: If n is a three-digit positive integer, what is the tens digit of n? [#permalink] New post   03 Nov 2019, 22:48
samstthomas wrote:
CAMANISHPARMAR wrote:
Question Stem:- n is a three-digit positive integer. To find - what is the tens digit of n
Important points:-
Its a value question.

STATEMENT 1:-

First find LCM 4 & 25 ---> 100. Check which all three digit numbers will give same remainder when divided by 100. e.g. 101, 102, 103, 201, 202, 203 ...... 901, 902, 903 etc. These are different numbers but look what the question stem is asking? Its asking for tens digit hence we have a definite value, its 0. hence statement 1 is sufficient.

We are down to A vs D.

Statement 2:-
Repeat the same process, First find LCM 16 & 25 ---> i.e. 400. Check which all three digit numbers will give same remainder when divided by 400. e.g. 401, 402, 403, .....414,415......... 801, 802, 803....814, 815.... etc. These are not only different numbers but this time we don't even have a tens digit which has a definite value, it can be 0 or 1. hence statement 2 is insufficient.

Hence the correct answer is A




Hi, for the statement A, if I chose the number as 150. The remainder is 2 when divisible by 4 and 25. In which, case the there are two outcomes isnt it? Please clarify


My dear friend, what is the remainder when 150 is divided by 25?
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32684
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If n is a three-digit positive integer, what is the tens digit of n? [#permalink] New post   29 Sep 2023, 07:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If n is a three-digit positive integer, what is the tens digit of n? [#permalink]
29 Sep 2023, 07:49
Moderator:
Bunuel
Math Expert
92933 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions